Which of the following equation(s) is/are correct on the of ideal gas equation?
where, $N =$ number of molecules, $N_{A} =$ Avogadro's number, $k_{B} =$ Boltzmann constant.

P V = \frac{N}{N_{A}} R T

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P V = N k_{B} T

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P V = \frac{d}{m} R T

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P V = d R T

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Solution

The correct options are
B $P V = \frac{N}{N_{A}} R T$
C $P V = N k_{B} T$
The equations of the options (A) and (B) are correct on the of ideal gas equation.
(A) $P V = \frac{N}{N_{A}} R T$
where $\frac{N}{N_{A}} = n =$ number of moles
(B) $P V = N k_{B} T$
Where $N k_{B} = n R$ as $k_{B} = \frac{R}{N_{A}}$ so $N k_{B} = \frac{N}{N_{A}} R = n R$
Also,
$P V = n R T = \frac{W}{M} R T$
$P M = \frac{W}{V} R T = d R T$

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